Tillis, who won the Republican Primary on Tuesday, has 45 percent of likely voters in North Carolina who say they support the Tarheel State's House speaker in the November midterms, and 44 percent who support the Democratic senator, in the poll taken May 7-8 of 750 likely voters in North Carolina. The poll has a margin of error of plus or minus 4 percentage points.

The poll found that 95 percent of North Carolina voters who have a very favorable opinion of Obamacare also support Hagan, while 86 percent of those with a very unfavorable view of the new healthcare law, which is a much larger share of voters, support Tillis.

Sixty-one percent of voters say it is unlikely that the problems with Obamacare will be fixed, with 36 percent saying it isn't likely at all, while only 31 percent think it is likely.

In addition, only 16 percent of North Carolina voters say they have been helped by the new healthcare law, while 35 percent say Obamacare has hurt them.

The matchup between Hagan and Tillis has remained close in previous surveys, which has shown the two contenders within two points of each other in all polls since March, according to Real Clear Politics.